Digitally modulated radio signals may experience degraded signal quality as a result of multipath fading over a terrestrial terrain, co-channel interference, and/or receiver noise corruption. Known probabilistic methods for the detection of such degraded signals include a maximum likelihood sequence estimation ("MLSE") based on the Viterbi algorithm to estimate a sequence of symbols, and use of an a posteriori probability ("MAP") algorithm to estimate an individual symbol.
MLSE is particularly suited for a sequence in which each symbol is contaminated by adjacent symbols in a time-dispersive transmission medium (intersymbol interference or "ISI"). Although the conventional MLSE algorithm provides an optimal estimate of a sequence of symbols, it does not readily provide the detection probability for each individual symbol which is desirable for the later decoding of the user information bits, assuming that a convolutional error correction code was used to generate the original information bits. Although various enhanced MLSE schemes have been proposed for deriving soft decision information in MLSE detection, such enhanced MLSE schemes are very computationally intensive or are otherwise impractical for many applications.
The conventional MAP algorithm does provide detection probability for each individual symbol, and is suited for any kind of received signal, whether or not ISI is present and whether or not the original signal was encoded with an error correction code. However, for a received signal corrupted by thermal noise at the receiver front-end (this noise is normally modeled as additive white Gaussian noise and has an exponential probability density function), estimation of each symbol typically requires a summation of multiple exponential terms, which results in a large dynamic range and is difficult to implement efficiently. In particular, when estimating a symbol from received sample(s) containing additive white Gaussian noise, the classic MAP algorithm calculates conditional probabilities in the form of exponential functions of the Euclidean distance between the received sample and its estimated one. This imposes a large dynamic range requirement for the detection apparatus and difficulties for efficiently implementing such an algorithm, especially if a fixed-point processor is used.
Approximations of the MAP algorithm are known in which processing is exclusively in the logarithmic domain, with the sum of two exponential functions being approximated by the function having the greater exponent. Although the required calculations are considerably simplified, such an approximation introduces an error which may be expressed as a function of the difference of two exponents and for which a suitable correction term may be stored in a pre-computed table.
A basic implementation of MAP symbol detection is shown in FIG. 1. It consists of a delay unit T, a symbol demodulator MAP, and a channel impulse response estimator IRE. Upon receiving a sample sequence {z.sub.k+L }, the MAP demodulator estimates a symbol {v.sub.k } from the estimated channel impulse response and all possibly transmitted symbols on the basis of maximum a posteriori probability. The channel impulse response estimator estimates the channel status by referring the received samples to a known symbol pattern, called the training sequence (such a sequence is normally available as a synchronization sequence in a time-multiplexing transmission scheme), or a prior symbol decision output from the MAP demodulator. Since normally the channel changes with time (for example, the fading typically experienced on a mobile radio channel), an updating algorithm (for example, the least-mean-square (LMS) algorithm, or the more fast convergent recursive-least-square (RLS) algorithm) is used to update the channel impulse response coefficients produced by the original estimation process, with the demodulated symbol decisions being used in the updated channel impulse response estimation. In this case, the decision made at a particularly time instant will lag the received symbol by several symbol periods (due to delay spread and the estimation lag), and a delay unit is used here to correlate the received symbol with the appropriate channel impulse response coefficients.
In some applications, the radio channel changes very little in a time-multiplexed transmission burst. In this case, only the symbols in the training pattern will be used for channel estimation. The channel parameters remain constant in the rest of symbol detection process. In some other applications where multiple synchronizations are employed the channel impulse response can be estimated from all the synchronization patterns and then they are interpolated to obtain channel parameters for data demodulation.
The digitally modulated signal transmitted over a terrestrial radio channel normally suffers from propagation loss, multipath fading, co-channel interference, and noise corruption. For a frequency-selective fading channel, the individual symbols transmitted will be spread out into their respective neighboring intervals and hence cause intersymbol interference (ISI). A demodulator is required in the baseband to recover the transmitted symbol at the possibly lowest detection error probability. For the frequency-selective fading channel where nulls exist in the received signal spectrum, an equalizer is needed to suppress ISI. At the same time, the equalizer shall not enhance noise around the frequency nulls. One commonly known technique for the above purpose is based on MAP (maximum a posteriori probability) and uses a so-called MAP demodulator, which suppresses the impairments and demodulates the transmitted symbols.
For radio applications, normally an error-correction code such as a convolutional code will be used in the system to further protect the symbols against transmission errors. At the receiver end, a decoder which follows the MAP demodulator is required to decode the information bits. For the convolutional code, soft decision decoding is highly preferred to hard-decision decoding because of the performance difference. Hence, the MAP demodulator is required not only to properly demodulate the transmitted symbols, but also provide soft decision reliability data to the decoder.
A classic MAP demodulator is shown in FIG. 2. In this demodulator, a recursive estimation process is employed to estimate each transmitted symbol. Specifically, upon receiving a new sample z.sub.k+L, sample estimator 10 generates estimated samples z.sub.k+L from the channel impulse response c(I) and the ideal symbols v.sub.k+I, where I=0, . . . , L and L represents the channel memory length. For a modulation scheme with a symbol alphabetic size of M, M.sup.L+1 estimates are required. Then an M.sup.L+1 -tuple probability function p(z.sub.k+L .vertline.v.sub.k+L, . . . , v.sub.k) is calculated in block 12. Those skilled in the art will recognize that this probability function is an exponential function of the negative of the Euclidean distance between the received sample and its estimated one, scaled by noise variance .sigma..sup.2. Then this probability function is multiplied (multiplier 14) with the M.sup.L -tuple function g(v.sub.k+L-1, . . . , v.sub.k) to yield a new function f(v.sub.k+L, . . . , v.sub.k). The function g(v.sub.k+L-1, . . . , v.sub.k) is calculated (block 16) by summing f(v.sub.k+L-1, . . . , v.sub.k-1) over v.sub.k-1, the function obtained from the previous iteration. Since the detection process is a recursive one, the calculated f(v.sub.k+L, . . . , v.sub.k) is delayed by one unit in delay 18 and stored for the next iteration.
Sequential additions are then performed over f(v.sub.k+L, . . . , v.sub.k) by adders 20 with respect to all possible symbols v.sub.k+L, . . . , v.sub.k+1, except v.sub.k. The resultant sums yield M probabilities, with each corresponding to one possible symbol. Then a selection is carried out (block 22) to find the maximum probability and the corresponding symbol, which becomes the detected symbol.
The calculated M probability values are also used in block 24 to derive soft decisions for the later stage of decoding. Normally, a bit likelihood ratio can be directly derived from these probability values. In the case of M-ary differential phase modulation, either the related symbol probability is used as the probability of each bit, or a mapping is carried out to calculate the likelihood ratio of each bit from all related symbol probabilities.